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Further remarks on elementary radicals and associated filters of ideals

Citation

Cojuhari, EP and Gardner, BJ, Further remarks on elementary radicals and associated filters of ideals, Bulletin of the Australian Mathematical Society, 103, (3) pp. 450-460. ISSN 0004-9727 (2021) [Refereed Article]

Copyright Statement

2020 Australian Mathematical Publishing Association Inc

DOI: doi:10.1017/S0004972720001021

Abstract

Ryabukhin showed that there is a correspondence between elementary radical classes of rings and certain filters of ideals of the free ring on one generator, analogous to the Gabriel correspondence between torsion classes of left unital modules and certain filters of left ideals of the coefficient ring. This correspondence is further explored here. All possibilities for the intersection of the ideals in a filter are catalogued, and the connections between filters and other ways of describing elementary radical classes are investigated. Some generalisations to nonassociative rings and groups are also presented.

Item Details

Item Type:Refereed Article
Keywords:radical class, radical filter
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Gardner, BJ (Dr Barry Gardner)
ID Code:145788
Year Published:2021 (online first 2020)
Deposited By:Mathematics
Deposited On:2021-08-05
Last Modified:2021-09-29
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